Gore compiled 107 yards on 19 carries, becoming the first player in San Francisco franchise history to record five consecutive 100-yard rushing performances.
The Redskins, meanwhile, dropped their fourth straight and fell to 3-5.
John Beck went 30-of-47 through the air for 254 yards, a touchdown and an interception, while Roy Helu made 14 grabs for 105 yards and added 41 rushing yards on 10 carries in the loss.
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